Finding a Basis Conversion Matrix via Prime Gauss Period Normal Basis

Yasuyuki NOGAMI  Ryo NAMBA  Yoshitaka MORIKAWA 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E92-A  No.6  pp.1500-1507
Publication Date: 2009/06/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
Keyword: 
public key cryptography,  extension field,  Gauss period normal basis,  basis conversion, 

Full Text: PDF(298.8KB)

Summary: 
This paper proposes a method to construct a basis conversion matrix between two given bases in Fpm. In the proposed method, Gauss period normal basis (GNB) works as a bridge between the two bases. The proposed method exploits this property and construct a basis conversion matrix mostly faster than EDF-based algorithm on average in polynomial time. Finally, simulation results are reported in which the proposed method compute a basis conversion matrix within 30 msec on average with Celeron (2.00 GHz) when mlog p≈160.